1. Field of the Invention
The disclosed invention relates to generally control systems, and more particularly to control systems using artificial intelligence to control a nonlinear plant.
2. Description of the Related Art
Feedback control systems are widely used to maintain the output of a dynamic system at a desired value in spite of external disturbance forces that would move the output away from the desired value. For example, a household furnace controlled by a thermostat is an example of a feedback control system. The thermostat continuously measures the air temperature of the house, and when the temperature falls below a desired minimum temperature, the thermostat turns the furnace on. When the furnace has warmed the air above the desired minimum temperature, then the thermostat turns the furnace off. The thermostat-furnace system maintains the household temperature at a constant value in spite of external disturbances such as a drop in the outside air temperature. Similar types of feedback control are used in many applications.
A central component in a feedback control system is a controlled object, otherwise known as a process xe2x80x9cplant,xe2x80x9d whose output variable is to be controlled. In the above example, the plant is the house, the output variable is the air temperature of the house, and the disturbance is the flow of heat through the walls of the house. The plant is controlled by a control system. In the above example, the control system is the thermostat in combination with the furnace. The thermostat-furnace system uses simple on-off feedback control to maintain the temperature of the house. In many control environments, such as motor shaft position or motor speed control systems, simple on-off feedback control is insufficient. More advanced control systems rely on combinations of proportional feedback control, integral feedback control, and derivative feedback control. Feedback that is the sum of proportional plus integral plus derivative feedback is often referred to as PID control.
The PID control system is a linear control system that is based on a dynamic model of the plant. In classical control systems, a linear dynamic model is obtained in the form of dynamic equations, usually ordinary differential equations. The plant is assumed to be relatively linear, time invariant, and stable. However, many real-world plants are time varying, highly nonlinear, and unstable. For example, the dynamic model may contain parameters (e.g., masses, inductances, aerodynamic coefficients, etc.) which are either poorly known or depend on a changing environment. If the parameter variation is small and the dynamic model is stable, then the PID controller may be sufficient. However, if the parameter variation is large, or if the dynamic model is unstable, then it is common to add adaptation or intelligent (AI) control to the PID control system.
AI control systems use an optimizer, typically a nonlinear optimizer, to program the operation of the PID controller and thereby improve the overall operation of the control system. The optimizers used in many AI control systems rely on a genetic algorithm. Using a set of inputs, and a fitness function, the genetic algorithm works in a manner similar to process of evolution to arrive at a solution which is, hopefully, optimal. The genetic algorithm generates sets of chromosomes (corresponding to possible solutions) and then sorts the chromosomes by evaluating each solution using the fitness function. The fitness function determines where each solution ranks on a fitness scale. Chromosomes which are more fit, are those chromosomes which correspond to solutions that rate high on the fitness scale. Chromosomes which are less fit, are those chromosomes which correspond to solutions that rate low on the fitness scale. Chromosomes that are more fit are kept (survive) and chromosomes that are less fit are discarded (die). New chromosomes are created to replace the discarded chromosomes. The new chromosomes are created by crossing pieces of existing chromosomes and by introducing mutations.
The PID controller has a linear transfer function and thus is based upon a linearized equation of motion for the plant. Prior art genetic algorithms used to program PID controllers typically use simple fitness functions and thus do not solve the problem of poor controllability typically seen in linearization models. As is the case with most optimizers, the success or failure of the optimization often ultimately depends on the selection of the performance (fitness) function.
Evaluating the motion characteristics of a nonlinear plant is often difficult, in part due to the lack of a general analysis method. Conventionally, when controlling a plant with nonlinear motion characteristics, it is common to find certain equilibrium points of the plant and the motion characteristics of the plant are linearized in a vicinity near an equilibrium point. Control is then based on evaluating the pseudo (linearized) motion characteristics near the equilibrium point. This technique works poorly, if at all, for plants described by models that are unstable or dissipative.
The present invention solves these and other problems by providing a new AI control system. Unlike prior AI control systems, the new AI control system is self-organizing and uses a new fitness (performance) function ƒ that is based on the physical law of minimum entropy. The self-organizing control system may be used to control complex plants described by nonlinear, unstable, dissipative models. The self-organizing control system further provides a physical measure of control quality based on physical law of minimum production entropy in an intelligent control system and in complex dynamic behavior control of a plant.
In one embodiment, the invention includes a method for controlling a nonlinear object (a plant) by obtaining an entropy production difference between a time differentiation (dSu/dt) of the entropy of the plant and a time differentiation (dSc/dt) of the entropy provided to the plant from a controller. A genetic algorithm that uses the entropy production difference as a fitness (performance) function evolves a control rule for a low-level controller, such as a PID controller. The nonlinear stability characteristics of the plant are evaluated using a Lyapunov function. The evolved control rule may be corrected using further evolutions.
In some embodiments, the control method may also include evolving a control rule relative to a variable of the controller by means of a genetic algorithm. The genetic algorithm uses a fitness function based on a difference between a time differentiation of the entropy of the plant (dSu/dt) and a time differentiation (dSc/dt) of the entropy provided to the plant. The variable may be corrected by using the evolved control rule.
In another embodiment, the invention comprises an AI control system adapted to control a nonlinear plant. The AI control system includes a simulator configured to use a thermodynamic model of a nonlinear equation of motion for the plant. The thermodynamic model is based on a Lyapunov function (V), and the simulator uses the function V to analyze control for a state stability of the plant. The AI control system calculates an entropy production difference between a time differentiation of the entropy of said plant (dSu/dt) and a time differentiation (dSc/dt) of the entropy provided to the plant by a low-level controller that controls the plant. The entropy production difference is used by a genetic algorithm to obtain an adaptation function in which the entropy production difference is minimized. The genetic algorithm provides a teaching signal to a fuzzy logic classifier that determines a fuzzy rule by using a learning process. The fuzzy logic controller is also configured to form a control rule that sets a control variable of the low-level controller.
In one embodiment, the low-level controller is a linear controller such as a PID controller. The learning processes may be implemented by a fuzzy neural network configured to form a look-up table for the fuzzy rule.
In yet another embodiment, the invention comprises a new physical measure of control quality based on minimum production entropy and using this measure for a fitness function of genetic algorithm in optimal control system design. This method provides a local entropy feedback loop in the control system. The entropy feedback loop provides for optimal control structure design by relating stability of the plant (using a Lyapunov function) and controllability of the plant (based on production entropy of the control system). The control system is applicable to all control systems, including, for example, control systems for mechanical systems, biomechanical systems, robotics, electro-mechanical systems, etc.